EXACT TWO-SAMPLE MEDIAN TESTS WHEN ONE "SAMPLE" VALUE POSSIBLY FROM A DIFFERENT POPULATION

Random samples are assumed for the univariate two-sample problem. Sometimes this assumption may be violated in that an observation in one “sample”, of size m, is from a population different from that yielding the remaining m—1 observations (which are a random sample). Then, the interest is in whether this random sample of size m—1 is from the same population as the other random sample. If such a violation occurs and can be recognized, and also the non-conforming observation can be identified (without imposing conditional effects), then that observation could be removed and a two-sample test applied to the remaining samples. Unfortunately, satisfactory procedures for such a removal do not seem to exist. An alternative approach is to use two-sample tests whose significance levels remain the same when a non-conforming observation occurs, and is removed, as for the case where the samples were both truly random. The equal-tail median test is shown to have this property when the two “samples” are of the same size (and ties do not occur).